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2 years ago

Use the quadratic formula to solve the equation 4x^2+6x-4=0

Mathematics

1 answer:

Vesnalui [34]2 years ago

4 0

Answer:

$\large\boxed{x=-2\ or\ x=\dfrac{1}{2}}$

Step-by-step explanation:

$\text{The quadratic formula of an equation}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{We have}\ 4x^2+6x-4=0\to a=4,\ b=6,\ c=-4.\\\\\text{Substitute:}\\\\x=\dfrac{-6\pm\sqrt{6^2-4(4)(-4)}}{2(4)}=\dfrac{-6\pm\sqrt{36+64}}{8}=\dfrac{-6\pm\sqrt{100}}{8}\\\\x=\dfrac{-6-10}{8}=\dfrac{-16}{8}=-2\ or\ x=\dfrac{-6+10}{8}=\dfrac{4}{8}=\dfrac{1}{2}$

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vichka [17]

Part A:

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Part B:

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2 years ago

Sherrod and Kamar are planning to drive at most 900 miles road trip. Sherrod drives at 60 miles per hour, and Kamar at 50 miles

Allushta [10]

The inequality gives the total expected journey from the road trip, such that the time during which Sherrod and Kamar drives is known.

a. The inequality that represents the miles that Sherrod and Kamar drives is; x + y ≤ 900

b. Two possible combination of x and y are; (600, 300) and (300, 600)

Reasons:

a. The distance distance Sherrod and Kamar plan to drive ≤ 900 miles

Sherrod's speed = 60 mph

Kamar's speed = 50 mph

The distance Sherrod drives = x

The distance Kamar drives = y

a. The miles driven by Sherrod and Kamar is given by the inequality;

x + y ≤ 900

b. Two possible combinations are;

First possible combination;

Sherrod drives for 10 hours, which gives;

Distance Sherrod drives = 60 mph × 10 hour = 600 miles

Kamar drives for 900 miles - 600 miles = 300 miles

Which gives;

Sherrod drives for 600 miles and Kamar drives for 300 miles

First combination; (600, 300)

Second possible combination;

The second possible combination is Sherrod drives for 300 miles and Kamar drives for 600 miles

Second combination; (300, 600)

Learn more about inequalities here:

brainly.com/question/22976364

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2 years ago

What is the length of the hypotenuse of the triangle?

masha68 [24]

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2 years ago

Read 2 more answers

ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.

pentagon [3]

Answer:

D. $f(x)=4x^{2}+1$

Step-by-step explanation:

There is a translation 1 point up along the y axis and a compression of 4.

Moving a function up (let's use h for the amount of points up) would change the function as so:

$f(x)=x^{2} +h$

Meanwhile, the compression would modify x in this case. You can eliminate any answers (A. and B.) that have no modification to x, and eliminate C., as a fraction modification would actually widen the graph instead of compress it.

Hope this helps! :]

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2 years ago

Please help I don’t know if I’m doing this correctly

solmaris [256]

Answers:

Exponential and increasing
Exponential and decreasing
Linear and decreasing
Linear and increasing
Exponential and increasing

=========================================================

Explanation:

Problems 1, 2, and 5 are exponential functions of the form $y = a(b)^x$ where b is the base of the exponent and 'a' is the starting term (when x=0).

If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.

If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.

In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.

Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.

---------------------

Problems 3 and 4 are linear functions of the form y = mx+b

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This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.

If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.

On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.

Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.

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